Why Might This Vector Product Question Be Considered Ambiguous?

[student34]

Homework Statement

It asks: Vector A has magnitude 2 and vector B has magnitude 3 with an angle between them equalling 0, 90 or 180. If the magnitude of A X B = 6, what angle/s must be between A and B?

The Attempt at a Solution

Knowing that the scalar product of the two vectors can also be considered a magnitude, I went with cos(0) or cos(180). But the answer is sin(90). I understand that that's what it would be if the question is asking for a vector product, but it didn't specify. I see how their answer is also right.

Am I misunderstanding something here? Or is it just known that the magnitude of the product of two vectors is the magnitude of the vector product and not of the scalar product?

 

[Michael Redei]

If the angle between two vectors is 0° or 180°, their cross product is a zero vector. So the angle between A and B must be the third alternative offered, i.e. 90°.

 

[TSny]

The symbol X in the product generally denotes a vector product. So if the statement of the problem had the product written as $A$ X $B$ then you would normally assume a vector product. A scalar product is usually denoted with a dot: $A\cdot B$

 

[student34]

The symbol X in the product generally denotes a vector product. So if the statement of the problem had the product written as $A$ X $B$ then you would normally assume a vector product. A scalar product is usually denoted with a dot: $A\cdot B$

Ahhhh, thank-you so much.